Computer aided engineering (CAE) has been used for supporting engineers in many tasks. For example, in a structure or product design procedure, CAE analysis, in particular finite element analysis (FEA), has often been employed to evaluate responses (e.g., stresses, displacements, etc.) under various loading conditions (e.g., static or dynamic).
FEA is a computerized method widely used in industry to simulate (i.e., model and solve) engineering problems relating to complex products or systems (e.g., cars, airplanes, etc.) such as three-dimensional non-linear structural design and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. The geometry is defined by elements and nodes. There are many types of elements, solid elements for volumes or continua, shell or plate elements for surfaces and beam or truss elements for one-dimensional structure objects. One of the most challenging simulations is related to contacts between two or more locations of the FEA model.
Simulating contacts have been mainly used in an impact event of two objects, for example, automobile crash, sheet metal forming, etc. Most of the prior art approaches have been focused on surface-to-surface contacts because automobiles and/or sheet metals are mainly modeled with shell elements (i.e., surface elements). As the advent of the computer power and technologies, more sophisticated engineering simulations are desired, for example, cables contained within a conduit, cables near a structural surface, human body modeling of muscles and tendons interacting with the skeleton, woven fabrics on a surface, etc. Many of these simulations require beam elements in contact with one or more surface meshes (i.e., a group of shell elements). Prior art approaches to simulate such contacts have been inadequate and inefficient, particularly when the surface mesh contains certain characteristics: for example, different sizes of shell elements, many different curvatures of small radius, arbitrary meshing (continuous or disjoint), and when the beam element's length is much larger than the surface mesh size.
To demonstrate the problems of prior art approaches, two examples are shown in FIGS. 1A and 1B (shown in two-dimension for illustration and visual simplicity). First, a beam element 110 is in contact with a surface 118 is shown in FIG. 1A. Because the beam element 110 is represented by two end nodes 112-114 in the prior art approaches, only two contacts can be detected between the beam element 110 and surface 118. Any contact between interior portion of the beam element 110 and the surface 118 is ignored. To further demonstrate the problem, FIG. 1B shows a beam element 120 is in contact with a surface 128 having many curvatures of small radius. Again only two contacts can be detected between the surface 128 and the beam element 120 at either end nodes 122-124. However, it is clear that there are three contacts between the beam element 120 and the surface 128. It would, therefore, be desirable to have an improved method and system that can be used for simulating beam-to-surface contacts more accurately and efficiently.